She greeted the new Canadian prime minister by saying it was "nice to see you again ... but under different circumstances."

"I will say, you were much taller than me the last time we met," replied Trudeau, who now towers over the monarch he first met as a child travelling with his father and prime minister at the time, Pierre Trudeau.

"Well, this is extraordinary to think of, isn't it," the Queen replied with a laugh.

The audience at the palace is his first stop on a week-long international trip that includes a midday speech to guests at Canada House, followed by an afternoon meeting with British Prime Minister David Cameron.

Trudeau will also attend the Commonwealth heads of government meeting in Malta that starts on Friday, and attend the first day of the Paris climate summit next week.

"So now you're having a very busy time," the Queen said to Trudeau, as cameras recorded the early moments of their meeting.

The Queen is well known for hergrasp of Canadian politics and history. She met with Pierre Trudeau several times while he was prime minister and reportedly enjoyed his company.

Speech highlights diversity

Trudeau also went to the Canadian High Commission. About 250 invited guests heard his speech at Canada House, including Bank of England governor (and former Bank of Canada governor) Mark Carney.

The Queen was "gracious and insightful, with a unique and valuable perspective," Trudeau told the crowd, according to the CBC's Rosemary Barton.

Prime Minister Justin Trudeau shakes hands with High Commissioner Gordon Campbell after being introduced at Canada House in London Wednesday. Campbell's 2011 appointment by Stephen Harper means his time in London will likely be over soon, with Trudeau expected to name a new high commissioner for the posting. (Adrian Wyld/Canadian Press)

Trudeau's remarks highlighted Canada's success at building an open, diverse and inclusive society, a message crafted to respond to the currently tense security situation following recent attacks by the Islamic State of Iraq and Syria (ISIS).

"As we renew our resolve to work with the international community to help prevent such attacks, and as we reaffirm our steadfast participation in the coalition against [ISIS], we must also recommit to building a world where diversity and difference are promoted and celebrated," Trudeau said.

The last election in Canada was about whether Canadians believe in those values, he said. Canada's pluralism is part of what defines it, he suggested, explaining that diversity overcomes hate.

Justin Trudeau on Canada's response to the Paris attacks at home1:05

He spoke of how as Canada opens its doors to more Syrians fleeing conflict in the coming weeks, "we are not just resettling refugees, we are welcoming new Canadians."

At the same time, his speech noted that for Canada's indigenous peoples, the Canadian reality is still not easy, equitable or fair, Barton reports.

Bilateral meeting with Cameron

Trudeau's first day in London concluded Wednesday afternoon with private talks at 10 Downing Street with Cameron.

Prime Minister Justin Trudeau holds his son and youngest of three children, Hadrien, as he arrives in London with his wife, Sophie Grégoire-Trudeau, and daughter Ella-Grace on Wednesday morning. After a quick change, the family was off to Buckingham Palace to meet the Queen. (Adrian Wyld/Canadian Press)

Prime ministers from Canada and the U.K. have generally gotten along well in the past. The two countries are some of the oldest and most stable continuous parliamentary democracies, and have a lot of common issues.

The two leaders discussed a range of topics, including climate change, trade, international security and the fight against ISIS, according to a media release. The meeting came just 12 days after the terrorist attacks in Paris.

The meeting comes at a crucial time as Cameron is set to make the case this week to the British Parliament that the U.K. should join other countries bombing ISIS militants in Syria.

The newly elected Canadian government has pledged to withdraw its six fighter jets from the bombing mission against ISIS, but has promised to continue to support the mission with increased training on the ground.

As Trudeau left Downing Street Wednesday evening, he told reporters in French his conversation with Cameron was a "very good" one.

The two leaders will get a chance to talk again when they're at the Commonwealth heads of government meeting in Malta.

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